Suspended Mass Calculator: Tension With a Sideways Pull, Stacked Masses and Submerged Loads

String tension for a mass pulled sideways, two hanging masses, and a load hanging in a liquid.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

Choose the case. For a mass pulled sideways the vertical component of the tension holds up the weight and the horizontal component balances the pull, so the tension is the square root of the weight squared plus the pull squared, and the string hangs at an angle whose tangent is the pull over the weight.

For two masses hanging one below the other, the lower string carries only the lower mass and the upper string carries both. Enter an upward acceleration to see the tensions rise when the load is accelerating upward, and fall when it accelerates downward.

For a submerged load, buoyancy (the weight of the liquid it pushes aside) reduces the tension. The calculator warns if the load is less dense than the liquid and floats.

Formulas used

  • T = \sqrt{(mg)^2 + F^2}
  • \tan\theta = \frac{F}{mg}
  • T = mg - \rho_{fluid}Vg

Worked example

With the default numbers in the calculator above:

  1. Weight: 49.05 N
  2. Balance of forces: vertical and horizontal: two equations, two unknowns
  3. Tension in the string: 52.97 N
  4. Angle of the string from the vertical: 22.18 °
  5. Pull needed to hold the string at your chosen angle: 17.85 N
  6. Tension at that angle: 52.20 N

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: Which case? Two masses hanging one below the other.

  1. Lower string (supports the lower mass only): 49.05 N
  2. Upper string (supports both masses): 147.15 N
  3. Check: the upper string carries the upper weight plus the lower string: 147.15 N

Common questions

Why is the tension more than the weight when pulled sideways?

Because the string has to hold up the weight and also balance the sideways pull, and the tension is the sum of those two as a vector.

What happens to the tension if the lift accelerates up?

The tension is m times (g plus a), so it is bigger than the weight. It is smaller if the acceleration is downward.

Does the string stretch?

The string is taken as light and not stretching.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Any first-year physics text (free-body diagrams, Newton's laws and buoyancy); Halliday, Resnick and Walker, Fundamentals of Physics.

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